If `(tan (alpha- beta+ gamma))/(tan (alpha+ beta- gamma))=(tan beta)/( tan gamma)`, show that either `sin (beta- gamma)=0` or `sin 2 alpha+ sin 2 beta+ sin 2 gamma=0`

If (tan(alpha+beta-gamma))/("tan"(alpha-beta+gamma))=(tangamma)/(tanbeta),(beta!=gamma) then sin2alpha+sin2beta+sin2gamma= (a) 0 (b) 1 (c) 2 (d) 1/2

If tan theta = ( tan alpha + tan beta)/(1 + tan alpha tan beta),"show that " sin 2 theta =(sin 2 alpha + sin 2 beta)/(1+sin 2 alpha sin 2 beta)

If sec alpha = sec beta sec gamma+ tan beta tan gamma , then show that sec beta= sec gamma sec alpha+- tan gamma tan alpha .

If tan theta = ( tan alpha - tan beta)/(1-tan alpha tan beta),"show that", sin 2 theta=(sin 2 alpha- sin 2 beta)/(1- sin2 alpha sin 2 beta).

If cos (beta - gamma) + cos (gamma - alpha) + cos (alpha - beta) = -3/2, "show that", cos alpha + cos beta + cos gamma = 0 "and" sin alpha + sin beta + singamma = 0."Hence deduce that," cos (beta - gamma) = cos (gamma - alpha) = cos (alpha - beta) = -1/2.

If alpha, beta and gamma are angle such that tan alpha + tan beta+tan gamma= tan alpha tan beta tan gammaand x=cos alpha + I sin alpha, y=cos beta+ I sin beta and z= cos gamma+ I sin gamma, then the value of xyz is -

If cos alpha+ cos beta+ cos gamma + cos alpha cos beta cos gamma=0 , show that sin alpha (1+ cos beta cos gamma)=+- sin beta sin gamma .

If alpha+ beta=(pi)/(2) and beta+ gamma= alpha then prove that tan alpha=tan beta+2 tan gamma .

If alpha, beta, gamma are positive acute angles, prove that sin alpha+sin beta+ sin gamma gt sin (alpha+ beta+ gamma)

If 2 sin alpha cos beta sin gamma =sin beta sin (alpha +gamma) then prove that tan alpha,tan beta,tan gamma are in H.P.